Question

Let p and q be the roots of the equation x² – 2x + A = 0 and let r and s be the roots of the equation x² – 18x + B = 0. If p < q < r < s are in arithmetic progression then the values of A and B are given by

• A. A = 3, B = 77
• B. A = 3, B = 7
• C. A = –3, B = 77
• D. A = 3, B = –7

Answer 1

Answer: (C)

A = –3, B = 77

Answer 2

Let the four numbers in A.P. be a – 3d, a – d, a + d and

a + 3d corresponding to the numbers p, q, r and s respectively.

We have p + q = 2, pq = A for x² – 2x + A = 0

and r + s = 18, rs = B for x² – 18x + B = 0.

Therefore p + q +r + s = 4a = 20 ⇒ a = 5.

Also p + q = 2 ⇒ 10 –4d = 2 ⇒ d = 2.

Hence the numbers are –1, 3, 7, 11.

Thus we have pq = A = –3 and rs = B = 77